Diurnal Cycle Model of Lake Ice Surface Albedo: A Case Study of Wuliangsuhai Lake

Ice surface albedo is an important factor in various optical remote sensing technologies used to determine the distribution of snow or melt water on the ice, and to judge the formation or melting of lake ice in winter, especially in cold and arid areas. In this study, field measurements were conducted at Wuliangsuhai Lake, a typical lake in the semi-arid cold area of China, to investigate the diurnal variation of the ice surface albedo. Observations showed that the diurnal variations of the ice surface albedo exhibit bimodal characteristics with peaks occurring after sunrise and before sunset. The curve of ice surface albedo with time is affected by weather conditions. The first peak occurs later on cloudy days compared with sunny days, whereas the second peak appears earlier on cloudy days. Four probability density distribution functions-Laplace, Gauss, Gumbel, and Cauchy-were combined linearly to model the daily variation of the lake ice albedo on a sunny day. The simulations of diurnal variation in the albedo during the period from sunrise to sunset with a solar altitude angle higher than 5 degrees indicate that the Laplace combination is the optimal statistical model. The Laplace combination can not only describe the bimodal characteristic of the diurnal albedo cycle when the solar altitude angle is higher than 5 degrees, but also reflect the U-shaped distribution of the diurnal albedo as the solar altitude angle exceeds 15 degrees. The scale of the model is about half the length of the day, and the position of the two peaks is closely related to the moment of sunrise, which reflects the asymmetry of the two peaks of the ice surface albedo. This study provides a basis for the development of parameterization schemes of diurnal variation of lake ice albedo in semi-arid cold regions.